An expression for Kinetic Energy

A change in kinetic energy of a mass over a path from point A to B will result from work done on the mass along this path, given that its potential does not change. From this statement, the familiar expression for kinetic energy will be produced.

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Since there is no natural frame of reference for measuring velocity, choose one such that the velocity at time t_a is zero.

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Considering the starting velocity of zero, the notation is simplified with delta T replaced simply by T.

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Now, noting that point B may represent any point, v(t_b) is simply called v, yielding the familiar expression for kinetic energy:

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